login
A123003
Expansion of g.f.: (8-29*x+24*x^2)/((1-4*x)*(1-3*x)*(1-2*x)^2*(1-x)^2).
2
8, 75, 463, 2394, 11274, 50265, 216581, 912648, 3788560, 15565095, 63484779, 257591862, 1041276566, 4197718965, 16888451857, 67845945636, 272258886492, 1091657974275, 4374492890615, 17521540911570, 70156842333538, 280839342481425, 1123993155149853
OFFSET
0,1
LINKS
E. Rodney Canfield and Herbert S. Wilf, Counting permutations by their runs up and down, arXiv:math/0609704 [math.CO], 2006; See u_4.
FORMULA
a(n) = (2*(n+1) + 1 - 16*(n-1)*2^n - 243*3^n + 64*4^(n+1))/4. - Greg Dresden, Jun 21 2021
MATHEMATICA
LinearRecurrence[{13, -67, 175, -244, 172, -48}, {8, 75, 463, 2394, 11274, 50265}, 23] (* Jean-François Alcover, Oct 08 2018 *)
PROG
(Magma) [(2*n + 3 - (n-1)*2^(n+4) - 3^(n+5) + 4^(n+4))/4: n in [0..30]]; // G. C. Greubel, Jul 12 2021
(Sage) [(2*n + 3 - (n-1)*2^(n+4) - 3^(n+5) + 4^(n+4))/4 for n in [0..30]] # G. C. Greubel, Jul 12 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 09 2006
STATUS
approved